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Wednesday 29th of June
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 Depdendent Variable

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 Dependent Variable

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# Exponential Growth

An exponential function of the form f(x) = bx has base b, where b is a real number, b > 0, and b 1.

An exponential growth function is an exponential function where b > 1. The graph of an exponential growth function increases when moving from left to right.

Letâ€™s look at the graphs of two exponential growth functions: f(x) = 2x and f(x) = 3x

Note:

Examples of exponential growth functions are population growth and compound interest earned on money invested.

From the graphs, notice the following:

â€¢ Each graph increases when moving from left to right (because b > 1).

â€¢ Both graphs intersect the y-axis at (0, 1).

â€¢ When x < 0, the graph of the function with the smaller base, y = 2x, lies above the graph of the function with the larger base, y = 3x.

â€¢ When x > 0, the graph of the function with the smaller base, y = 2x, lies below the graph of the function with the larger base, y = 3x.

â€¢ Each graph passes the vertical and horizontal line tests. Therefore, each graph represents a one-to-one function.

â€¢ The domain of each function is all real numbers.

â€¢ The range of each function is all positive real numbers.